Mathematical modelling of one-dimensional morphological changes in rivers with non-uniform sediment

Abstract

The present study is aimed at the development of a mathematical model for the prediction of one-dimensional morphological changes (erosion/sedimentation) in alluvial rivers with nonuniform sediment.In the model the river bed is schematized into a moving top layer (transport layer), of which the grain-size distribution is determinative for the sediment transport, and a non-moving underlayer which generally contains sediment with a different grain-size distribution (one-layer model).In order to verify this model, an experimental study was set up in laboratory conditions with a moderately graded sediment mixture of two grain sizes.Initially, a series of experiments was carried out in steady and uniform ('equilibrium') conditions in order to obtain suitable empirical components of the mathematical model, such as a transport formula (per size fraction) and predictors for the bed roughness and transport layer thickness.In addition, detailed information was gathered about the behaviour of the different grain sizes in the upper layers of the bed, using a refined bed-sampling technique.Because of vertical sorting and the irregular character of the bed forms (dunes), there was a vertical exchange of grain sizes between upper and lower layers of the bed.An experiment was then carried out in 'non-equilibrium' conditions which indicated that the changes in bed composidon could not be described adequately by the one-layer model.Based on this finding and the observed vertical exchange mechanism, a two-layer theory was developed and implemented numerically.Contrary to the one-layer theory, this theory includes a vertical exchange-process between the top layer (transport layer) and an exchange layer.Mathematical analysis indicated that this model has a more attractive mathematical character than the one-layer model.Moreover, an improved agreement was obtained with the measurements.Finally, a short study was made of a morphological problem in the River Meuse in the Netherlands (a bend cut-off and a flow constriction), in order to illustrate the importance of modelling of time-dependent changes in grain-size composition in field conditions.